2D Geometry Questions and Answers

In the figure below mJKM 92 KL bisects JKM and KN bisects LKM Find mZMKM m2NKM

1 4 Notetaking with Vocabulary continued In Exercises 9 14 use the diagram 9 Find the perimeter of AABD 10 Find the perimeter of ABCD 11 Find the perimeter of quadrilateral ABCD 12 Find the area of AABD 13 Find the area of ABCD 14 Find the area of quadrilateral ABCD D 4 1 C 1 5 Ay 2 A 2 4 4 x B 2 1

18 Do you remember the daisy construction from Chapter 0 Construct a circle with radius s With the same compass setting divide the circle into six congruent arcs Construct the chords to form a regular hexagon inscribed in the circle Construct radii to each of the six vertices What type of triangle is formed What is the ratio of the perimeter of the hexagon to the diameter of the circle

9 Sketch the path made by the midpoint of a radius of a circle if the radius is rotated about the center

25 A 38 40 a 9 72 m b 11 8 m

24 C 68 5 c 258 cm b 386 cr

23 B 72 2 b 78 3 m c 145 m

3 For which pair of figures can Figure Y a Pair 1 b Pair 2 A c Pair 3 Z A Pair 1 B B Z joue beenwoh etinu ewol s syslane T O 4 Refer to the three pairs of figures shown For each pair of figures determine which single transformation translation rotation or reflection maps Figure A onto Figure B C M Z Pair 2 B sagrit to main Shoillaog A hupit s toolog A iubit alsio 8 ods Balvolbolo Pair 3 00 A B

5 Draw the image of the quadrilateral shown after a 180 clockwise rotation about point al pupil vow nislax P

graph of the function y 2 was transformed according to the transformations given below resulting in the graph of the function y a z b c for some constants a b and c 1 reflection over the x axis 2 vertical shrink 3 horizontal shift left 4 vertical shift up Eleanor was asked to provide a possible value for a b and c She said a Determine if each of her values are reasonable and give reasons for your answers 10 Using the graph of g x shown sketch the transformation g x 2 on the same coordinate grid 4 4 43 1 5 3 O M b 4 and c 7 2 3 4 10

Write an inequality in slope intercept form from the linear inequality graphed below y 10 10 8 64 2 8 6 4 2 24 008 8 4 6810

144 5 4 56 3 2 m 1 m42 m43 m24 m25

The owner of a convenience store installs two security cameras represented by points C1 and C2 Both cameras point towards the centre of the store s cash register represented by the point R The following diagram shows this information on a cross section of the store 2 8 1 0 6 4 diagram not to scale C2 3 1 The cameras are positioned at a height of 3 1 m and the horizontal distance between the cameras is 6 4 m The cash register is sitting on a counter so that its centre R is 1 0 m above the floor The distance from Camera 1 to the centre of the cash register is 2 8 m Determine the angle of depression from Camera 1 to the centre of the cash register Gi

For Exercises 2 9 use the diagram at right Points E P and is the center of the circle 2 Name three chords 3 Name one diameter 4 Name five radii 5 Name five minor arcs 6 Name two semicircles 7 Name two major arcs 8 Name two tangents 9 Name a point of tangency 10 Name two types of vehicles that use wheels two household appliances that use wheels and two uses of the wheel in the world of entertainment H A E B P F C G

K P K M N N 4 Here is quadrilateral KLMN after a rotation around M KLMN and its image degree counterclockwise

17 BLUE FISH F H 6 E 6 B U L 6 18 RECTANGL G R T C 12 did in 19 Imagine using two congruent triangles to create a special quadrilateral as you the investigation a What type of triangles do you need to form a rectangle Explain b What type of triangles do you need to form a square Explain

B 6 A 3 A X E 4 D Yukar daki ekilde m BAD g re AE x ka cm dir C B 4 C 5 ABC bir ikizkenar gen AB AC AD BC ED 4 cm BD 6 cm m DCE oldu una D 6 E 8 00

If U I Y point I is between points U and Y and IY 3 1 and UY 91 find UI

What does the notation Rx axis DAB mean Reflection Rotation Clockwise Counter clockwise Around the origin to the axis Over the x axis Over the y axis 180 90 270

In the figure below C is between A and D and B is the midpoint of AC If BC 4 and AD 11 find CD CD 1 D X 5

8 To estimate the weight of pumpkins for the pumpkin farm a farmer took a random sample of 30 pumpkins The weights to the nearest tenth of a pound of those 30 randomly sampled pumpkins is given by the table below Answer each question 12 pts 2 5 17 0 7 3 4 0 7 9 8 0 11 9 12 0 15 9 16 0 19 9 9 1 13 4 14 4 A Construct a histogram for the number of victories Use the following classes Label your graph as needed 3 pts 0 3 9 16 7 3 1 5 1 9 3 6 0 2 4 6 0 10 3 19 Shape Center Spread B Identify the five number summary to the nearest undredth 1 pt 1 9 5 6 12 0 D Create a boxplot for the number of victories You can place your boxplot anywhere on the vertical portion of the graph 3 pts 10 8 6 4 2 0 9 5 y 505 6 8 8 4 0 Frequency 4 10 3 12 8 9 9 4 8 18 3 7 6 8 Pumpkin Weight lbs C Identify the mean and standard deviation to the nearest hundredth 1 pt 4 8 12 16 Pumpkin Weight lbs E Describe the shape center spread and unusual features for the weights of the pumpkins 4 pts 5 6 2 6 15 1 12 16 20 X ix 20

1 point A hula hoop has a radius of 19 inches What is the length of the arc subtending 1 4 of the hoop 59 7 inches 29 8 inches 14 9 inches 43 8 inches

B 1 point A circle has a circumference of 28 centimeters If an arc subtends a central angle of 55 degrees what is the arc length 8 56 centimeters 26 88 centimeters 53 76 centimeters 4 28 centimeters

5 1 point Area of sector is to O circumference of circle circle area diameter semicircle as arc measure is to 360 degrees

9 1 point A pizza has a radius of 7 inches If it is cut into 6 equal slices what is the area of each slice 7 33 square inches 14 66 square inches 49 square inches 25 66 square inches Previous

1 1 point A plane slices through a cone parallel to the base What shape is the cross section oval triangle square circle 0000

7 1 point How many radians are in a semicircle 00 T EN EN 3 01 2 2

3 1 point A sector of a circle has a central angle measure of 310 degrees If the radius of the circle is 2 feet what is the area of the sector 12 31 square feet 10 82 square feet 5 41 square feet 21 64 square feet 000

to the coordinate grid 5 4 Find point Q on RS that is of the distance from R to S 8 3 5 Find point D on AB that is of the distance from A to B 6 Find point G on AB such that the ratio of AG to GB is 3 2 A R Ay O U M M B S M

d y 46 O C 4 d y 4 b 2 y 4 2 T b do not shift up or down do not shift left or right shrink vertically neither stretch nor shrink horizontally a shrink vertically neither stretch nor shrink horizontally do not shift up or down Shift lefUright a 4 d 4 c by a factor of by a factor of 6 by a factor of by a factor of X 6 by a factor of by a factor of units units 4 units units O 4 units C C a y How is the graph in part b related to the graph in part a If a graph is not supposed to be stretched or shrunk enter 1 in the corresponding box on the right If a graph is not supposed to be shifted in some direction enter 0 in the corresponding box on the righ Do not reflect a 12 b b d 4 How is the graph in part c related to the graph in part a If a graph is not supposed to be stretched or shrunk enter 1 in the corresponding box on the right If a graph is not supposed to be shifted in some direction enter 0 in the corresponding box on the right Reflect across the x axis d 6 X X How is the graph in part d related to the graph in part a If a graph is not supposed to be stretched or shrunk enter 1 in the corresponding box on the right If a graph is not supposed to be shifted in some direction enter 0 in the corresponding box on the right Reflect across the x axis shrink vertically neither stretch nor shrink horizontally do not shift up or down

through f P x x 5 1 a Give the coordinates of the vertex The coordinates of the vertex are Type an ordered pair 10 8 2 8 16 4 2 4

the following quadratic function a write the function in the form P x a x h 2 k b give parabola and c graph the function P x 3x 9x P x se integers or fractions for any numbers in the expression

Match the point in polar coordinates OB 2 3x 6 oc 2 2 OD 2 X 2 7 to to the points A B C or D 5

Graph all asymptotes of the rational function f x x 2x 3 x 2 H X

State the coordinates for each of the plotted points Enter your answers in form of ordered pairs like x y Do not forget the parentheses M E A B C D 5 4 3 2 1 AO 002 5 4 3 2 1 1 C 2 3 BO 5 1 2 3 4 5

Write an equation for the line graphed below y 19 V F

2 52 3 5 47 m21 m 2 m43 m24 m25

Use the Law of Cosines to solve the triangle Round your answers to two decimal places A B C O O O b 7 A c 15 a 11 B

Find the exact values of the remaining trigonometric functions of 0 satisfying the given conditions If an answer is undefined enter UNDEFINED csc 6 cot 0 0 sin 8 cos 0 tan 8 sec 0 cot 0

15 ACAR APET 5 Co y 6 6 R P A 5 E 16 TUNA FISH DMIMOZA X 7 T U 6 6 N H

11 For which value of x is line parallel to line 12 For which value of x is line parallel to m line m X X 13 For which value of x is line parallel to line m 15 3x 20 110 2x 10 1 X X 53 8x 9y 14 For which value of x is line n parallel to line m p 30 80 x m q m

3 1 point The city of Covington is placing a statue in a triangular grassy area bounded by sidewalks on all 3 sides If the city wants the statue to be an equal distance from all 3 sides of the grassy area where should they place it at the orthocenter of the triangle at the centroid of the triangle at the incenter of the triangle at the circumcenter of the triangle

1 point Ed is constructing the perpendicular bisector of a segment on his paper He just finished labeling the points of intersection of the two arcs that he drew What is his next step Oopen the compass to more than half the length of the segment but less than the whole length draw an arc with a radius length equal to the segment length construct the line connecting the two points draw two arcs using each of the endpoints as centers

20 1 point An inscribed circle is not related perpendicular to tangent to equal to O DOO Previous all 3 sides of the triangle it is inscribed in

17 1 point A quadrilateral inscribed in a circle is called a bilateral quadrilateral central quadrilateral connected quadrilateral cyclic quadrilateral OO

11 1 point R 102 m S T What is the measure of arc RST 204 degrees 102 degrees 51 degrees 180 degrees

1 point Kris has 3 daughters who all live in different cities across Georgia She wants to live somewhere that is an equal distance from each of her daughters She mapped out the 3 cities and drew a triangle connecting them How can she find a point on the map that is an equal distance from all 3 cities construct the circumcenter estimate the best place construct the incenter construct the orthocenter

8 1 point C 5 B Segments AB and BC are both tangent to the circle shown above What is the length of BC Note photo not necessarily to scale 10 25 2 5

1 point Line I is tangent to circle Q What is the measure of the angle formed at the point of tangency 180 degrees 90 degrees 45 degrees 100 degrees

3 1 point E 10 5 C Solve for x x 10 x 5 x 7 5 x 15 Previous Xx D